The Corynespora leaf fall disease of rubber trees, caused by the necrotrophic fungus Corynespora cassiicola, is responsible for important yield losses in Asian and African plantations, whereas its impact is negligible in South America. The objective of this study was to identify potential antagonists of C. cassiicola among fungal endophytes (i.e., Pestalotiopsis, Colletotrichum, and Trichoderma spp.) isolated from wild and cultivated rubber trees distributed in the Peruvian Amazon. We first tested the endophytes in dual in vitro confrontation assays against a virulent C. cassiicola isolate (CCP) obtained from diseased rubber trees in the Philippines. All Trichoderma isolates overran the CCP colony, suggesting some antagonistic mechanism, while species from the other genera behaved as mutual antagonists. Trichoderma isolates were then tested through antibiosis assays for their capacity to produce growth-inhibiting molecules. One isolate (LA279), recovered as an endophyte from a wild Hevea guianensis specimen and identified as Trichoderma koningiopsis, showed significant antibiosis capacity. We demonstrated that LA279 was also able to endophytically colonize the cultivated rubber tree species (H. brasiliensis). Under controlled laboratory conditions, rubber plants were inoculated with three Trichoderma strains, including LA279, in combination with the pathogenic CCP. Results showed that 1 week preinoculation with the endophytes differentially reduced CCP mycelial development and symptoms. In conclusion, this study suggests that T. koningiopsis isolate LA279—and derivate compounds—could be a promising candidate for the biological control of the important rubber tree pathogen C. cassiicola.